Radiative transfer is analyzed for participating media consisting of long cylindrical fibers with a diameter in the limit of geometrical optics (Fig. 1). The absorption and scattering coefficients and the scattering phase function of the medium are determined based on the discrete-level medium geometry and optical properties of the fiber material. The fibers are assumed to be randomly oriented and positioned inside the medium. Three approaches are employed: a combined volume-averaging and Monte Carlo ray-tracing technique, a combined mean-free path and Monte Carlo ray-tracing technique, and an analytical approach recently developed for packed bed of spheres and adapted here to long fibers.
The radiative properties obtained by the three methods are used to solve to compute the overall transmittance and reflectance of the medium, and the results are validated against predictions by the direct Monte Carlo simulation. The effects of volume fraction and optical properties of fibers on the medium radiative properties and the overall slab radiative characteristics are investigated.